E-Math 2023 Worked Solutions

Ratio (sharing a quantity)

2 marks · number & algebra (ratio)

Obtuse-angle trig ratios

3 marks: 2 + 1 · geometry & measurement (trig values, radians)

Laws of indices

3 marks: 1 + 2 · number & algebra (indices)

Prime factorisation

3 marks: 1 + 1 + 1 · number & algebra (primes, cubes, lcm)

Compound interest

3 marks: 1 + 2 · number & algebra (compound interest)

Completing the square

3 marks: 2 + 1 · number & algebra (completing the square)

Percentage increase

5 marks: 2 + 3 · number & algebra (percentage)

Cumulative frequency curve (median

6 marks: (a) 1 + 2, (b) 1, (c) 1 + 1 · statistics (cumulative frequency, mean, s.d.)

Currency exchange / rate

2 marks · number & algebra (currency / rate)

Coordinate geometry (gradient formula)

2 marks · number & algebra (coordinate geometry)

Algebraic fractions (subtraction)

2 marks · number & algebra (algebraic fractions)

Common-factor

5 marks: (a) 1 + 2, (b) 2 · number & algebra (factorising, expansion)

Probability of a single event (forming an equation)

2 marks · statistics & probability

Angle in a semicircle

2 marks · geometry & measurement (circle / angle reasoning)

Factorising to prove divisibility

3 marks · number & algebra (algebraic proof)

Ratio of volumes of similar solids

1 mark · geometry & measurement (similar solids, reasoning)

Venn-diagram shading

2 marks: 1 + 1 · number & algebra (set language)

Similar cones (linear relation of radius and height)

4 marks: 1 + 3 · geometry & measurement (similar cones, volume)

Quadratic graph from factorised form

2 marks · number & algebra (quadratic graph sketch)

Factorising a quadratic

3 marks · number & algebra (algebraic fractions / difference of squares)

Matrix product (order & dimensions)

5 marks: 2 + 2 + 1 · number & algebra (matrices)

Forming equations from area & perimeter

5 marks: 2 + 3 · number & algebra (area & perimeter equations)

Bearings & back bearings

7 marks: 1 + 3 + 3 · geometry & measurement (bearings, cosine & sine rules)

Inverse proportion (inverse square)

3 marks: 2 + 1 · number & algebra (inverse proportion)

Term from the sum Tn=Sn-Sn-1

3 marks: 2 + 1 · number & algebra (sequences from sn)

Face diagonal

4 marks · geometry & measurement (3-d / space diagonal)

Position/route vectors

5 marks: 2 + 3 · number & algebra (vectors)

Standard form

10 marks: (a) 1 + 2 + 2, (b) 2, (c) 2 + 1 · number & algebra (standard form, percentage, scale)

Linear equations

12 marks: (a) 2, (b) 1, (c) 1 + 3, (d) 5 · number & algebra (equations, inequality, change of subject)

Surface area of sphere/hemisphere

9 marks: 2 + 3 + 4 · geometry & measurement (mensuration: hemisphere & cylinder)

Completing a table of values

11 marks: (a) 1, (b) 3, (c) 2 + 2 + 3 · number & algebra (graphs of functions)

Tangent-radius

8 marks: 4 + 4 · geometry & measurement (circle properties, tangent, arc length)

Vector combination → simultaneous equations

11 marks: (a) 4, (b) 1 + 2 + 4 · number & algebra (vectors & coordinate geometry)

Box-and-whisker plots (quartiles

9 marks: (a) 1 + 3, (b) 1 + 2 + 2 · statistics & probability

Number-grid patterns

10 marks: (a) 3 + 3, (b) 4 · number & algebra (number patterns, sequences)

Energy = power × time

10 marks: 1 + 2 + 7 · number & algebra / statistics (real-world modelling)